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Part 1 of 8 · quant-ph
Microscopic Distinguishability and the Data of Geometric Reconstruction
What geometric data are actually fixed by distinguishability?
What this part establishes
The relative-entropy Hessian is the BKM metric, while Bures and SLD metrics require separate conventions. A Lorentzian reconstruction needs localization and causal data beyond a positive information metric.
Boundary of the claim
It does not construct spacetime from an arbitrary density matrix.